Signature of Einstein-Cartan theory

TL;DR

This paper investigates how spacetime torsion, as predicted by Einstein-Cartan theory, affects spin-polarized particles, proposing observable effects that could differentiate it from standard general relativity.

Contribution

It derives a non-relativistic Hamiltonian incorporating torsion effects and identifies measurable spin polarization deviations as potential evidence for Einstein-Cartan theory.

Findings

Deviations in spin polarization can distinguish Einstein-Cartan from general relativity

Derived a non-relativistic Hamiltonian including torsion effects

Proposed experimental signatures for detecting spacetime torsion

Abstract

We study the physical effects of torsion as predicted by the Einstein-Cartan theory in the test particle approximation and the non-relativist limit. We first present the corresponding non-relativistic Hamiltonian for a 2-spinor. Then, we solve an idealized reflection and transmission problem for a non-relativistic spin-$\frac{1}{2}$ beam travelling across a spin-polarized target. We identify deviations in the spin polarizations of the reflected and transmitted as observables capable of distinguishing Einstein-Cartan from standard general relativity. If measured, this effect would constitute compelling evidence for the presence of spacetime torsion.